Search results for: Johnson-Cook material model

Authors: Kuen-Ming Shu, Cheng-Yu Chen

Abstract:

A vibrating-fork sensor can measure the level height of solids and liquids and operates according to the principle that vibrations created by piezoelectric ceramics are transmitted to the vibrating fork, which produces resonance. When the vibrating fork touches an object, its resonance frequency changes and produces a signal that returns to a controller for immediate adjustment, so as to effectively monitor raw material loading. The design of the vibrating fork in a vibrating-fork material sensor is crucial. In this paper, ANSYS finite element analysis software is used to perform modal analysis on the vibrations of the vibrating fork. In addition, to design and produce a superior vibrating fork, the dimensions and welding shape of the vibrating fork are compared in a simulation performed using the Taguchi method.

Keywords: Vibrating fork, piezoelectric ceramics, sound wave, ANSYS, Taguchi method, modal analysis.

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Authors: G. Korotcenkov, V. Brinzari, B. K. Cho

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The thermoelectric properties of nano-scaled In₂O₃:Sn films deposited by spray pyrolysis are considered in the present report. It is shown that multicomponent In₂O₃:Sn-based films are promising material for the application in thermoelectric devices. It is established that the increase in the efficiency of thermoelectric conversion at C_Sn~5% occurred due to nano-scaled structure of the films studied and the effect of the grain boundary filtering of the low energy electrons. There are also analyzed the limitations that may appear during such material using in devices developed for the market of thermoelectric generators and refrigerators. Studies showed that the stability of nano-scaled film’s parameters is the main problem which can limit the application of these materials in high temperature thermoelectric converters.

Keywords: Energy conversion technologies, thermoelectricity, In2O3-based films, power factor, nanocomposites, stability.

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Authors: Dursun Aydın

Abstract:

In this paper, estimation of the linear regression model is made by ordinary least squares method and the partially linear regression model is estimated by penalized least squares method using smoothing spline. Then, it is investigated that differences and similarity in the sum of squares related for linear regression and partial linear regression models (semi-parametric regression models). It is denoted that the sum of squares in linear regression is reduced to sum of squares in partial linear regression models. Furthermore, we indicated that various sums of squares in the linear regression are similar to different deviance statements in partial linear regression. In addition to, coefficient of the determination derived in linear regression model is easily generalized to coefficient of the determination of the partial linear regression model. For this aim, it is made two different applications. A simulated and a real data set are considered to prove the claim mentioned here. In this way, this study is supported with a simulation and a real data example.

Keywords: Partial Linear Regression Model, Linear RegressionModel, Residuals, Deviance, Smoothing Spline.

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Authors: Francisca Grimón, Marylin Giugni, Josep Monguet F., Joaquín Fernández, Luis León G.

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In blended learning environments, the Internet can be combined with other technologies. The aim of this research was to design, introduce and validate a model to support synchronous and asynchronous activities by managing content domains in an Adaptive Hypermedia System (AHS). The application is based on information recovery techniques, clustering algorithms and adaptation rules to adjust the user's model to contents and objects of study. This system was applied to blended learning in higher education. The research strategy used was the case study method. Empirical studies were carried out on courses at two universities to validate the model. The results of this research show that the model had a positive effect on the learning process. The students indicated that the synchronous and asynchronous scenario is a good option, as it involves a combination of work with the lecturer and the AHS. In addition, they gave positive ratings to the system and stated that the contents were adapted to each user profile.

Keywords: Blended Learning, System Adaptive, Model, Clustering Algorithms.

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Authors: Mahsa Shafaei Bajestani, Mahmoud Yazdani, Aliakbar Golshani

Abstract:

Artificial lightweight aggregates have a wide range of applications in industry and engineering. Nowadays, the usage of this material in geotechnical activities, especially as backfill in retaining walls has been growing due to the specific characteristics which make it a competent alternative to the conventional geotechnical materials. In practice, a material with lower weight but higher shear strength parameters would be ideal as backfill behind retaining walls because of the important roles that these parameters play in decreasing the overall active lateral earth pressure. In this study, two types of Light Expanded Clay Aggregates (LECA) produced in the Leca factory are investigated. LECA is made in a rotary kiln by heating natural clay at different temperatures up to 1200 °C making quasi-spherical aggregates with different sizes ranged from 0 to 25 mm. The loose bulk density of these aggregates is between 300 and 700 kN/m³. The purpose of this research is to determine the stress-strain behavior, shear strength parameters, and the energy absorption of LECA materials. Direct shear tests were conducted at five normal stresses of 25, 50, 75, 100, and 200 kPa. In addition, conventional triaxial compression tests were operated at confining pressures of 50, 100, and 200 kPa to examine stress-strain behavior. The experimental results show a high internal angle of friction and even a considerable amount of nominal cohesion despite the granular structure of LECA. These desirable properties along with the intrinsic low density of these aggregates make LECA as a very proper material in geotechnical applications. Furthermore, the results demonstrate that lightweight aggregates may have high energy absorption that is excellent alternative material in seismic isolations.

Keywords: Expanded clay, direct shear test, triaxial test, shear properties, energy absorption.

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Authors: Tian Hai, Yang Shengsheng, Jr., Wang Yi

Abstract:

Based on an analysis of the mechanism of degradation of optical characteristics of the ZnO-pigmented white paint by electron irradiation, a model of single molecular color centers is built. An equation that explains the relationship between the changes of variation of the ZnO-pigmented white paint-s spectrum absorptance and electron fluence is derived. The uncertain parameters in the equation can be calculated using the curve fitting by experimental data. The result indicates that the model can be applied to predict the degradation of optical characteristics of ZnO-pigmented white paint by electron radiation.

Keywords: ZnO-pigmented white pain, effects of electron radiation, optical characteristics degradation, prediction model.

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Authors: Zuodong Liang, Dong-Sheng Jeng

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Seabed instability around an offshore pipeline is one of key factors that need to be considered in the design of offshore infrastructures. Unlike previous investigations, a three-dimensional numerical model for the wave-induced soil response around an offshore pipeline is proposed in this paper. The numerical model was first validated with 2-D experimental data available in the literature. Then, a parametric study will be carried out to examine the effects of wave, seabed characteristics and confirmation of pipeline. Numerical examples demonstrate significant influence of wave obliquity on the wave-induced pore pressures and the resultant seabed liquefaction around the pipeline, which cannot be observed in 2-D numerical simulation.

Keywords: Pore pressure, 3D wave model, seabed liquefaction, pipeline.

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Authors: Ruedee Niyomrath

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The purposes of this research is aim to build the energy saving stove for stew coconut sugar. The research started from explores ceramic raw materials in local area, create the appropriate mixture of ceramic raw materials for construction material of stove, and make it by ceramic process. It includes design and build the energy saving stove, experiment the efficiency of energy saving stove as to thermal efficiency, energy saving, performance of time, and energy cost efficiency, transfer the knowledge for community, stove manufacturers, and technicians. The findings must be useful to the coconut sugar enterprises producing, to reduce the cost of production, preserve natural resources, and environments.

Keywords: Ceramic raw material, Energy saving stove, Stove design, Performance of stove, Stove for stew coconut sugar.

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Authors: L. Novakova-Marcincinova, J. Novak-Marcincin

Abstract:

Paper presents knowledge about types of test in area of materials properties of selected methods of rapid prototyping technologies. In today used rapid prototyping technologies for production of models and final parts are used materials in initial state as solid, liquid or powder material structure. In solid state are used various forms such as pellets, wire or laminates. Basic range materials include paper, nylon, wax, resins, metals and ceramics. In Fused Deposition Modeling (FDM) rapid prototyping technology are mainly used as basic materials ABS (Acrylonitrile Butadiene Styrene), polyamide, polycarbonate, polyethylene and polypropylene. For advanced FDM applications are used special materials as silicon nitrate, PZT (Piezoceramic Material - Lead Zirconate Titanate), aluminium oxide, hydroxypatite and stainless steel.

Keywords: Rapid prototyping, materials, testing of materials.

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Authors: Aboagela Dogman, Reza Saatchi, Samir Al-Khayatt

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In this study, a network quality of service (QoS) evaluation system was proposed. The system used a combination of fuzzy C-means (FCM) and regression model to analyse and assess the QoS in a simulated network. Network QoS parameters of multimedia applications were intelligently analysed by FCM clustering algorithm. The QoS parameters for each FCM cluster centre were then inputted to a regression model in order to quantify the overall QoS. The proposed QoS evaluation system provided valuable information about the network-s QoS patterns and based on this information, the overall network-s QoS was effectively quantified.

Keywords: Fuzzy C-means; regression model, network quality of service

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Authors: Yanling Zhu, Kai Wang

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In this paper, by utilizing the coincidence degree theorem a predator-prey model with modified Leslie-Gower Hollingtype II schemes and a deviating argument is studied. Some sufficient conditions are obtained for the existence of positive periodic solutions of the model.

Keywords: Predator-prey model, Holling II type functional response, positive periodic solution, coincidence degree theorem.

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Authors: E. Hajizadeh, H. Garmabi

Abstract:

Toughening of polyamide 6 (PA6)/ Nanoclay (NC) nanocomposites with styrene-ethylene/butadiene-styrene copolymer (SEBS) using maleated styrene-ethylene/butadiene-styrene copolymer (mSEBS)/ as a compatibilizer were investigated by blending them in a co-rotating twin-screw extruder. Response surface method of experimental design was used for optimizing the material and processing parameters. Effect of four factors, including SEBS, mSEBS and NC contents as material variables and order of mixing as a processing factor, on toughness of hybrid nanocomposites were studied. All the prepared samples showed ductile behavior and low temperature Izod impact toughness of some of the hybrid nanocomposites demonstrated 900% improvement compared to the PA6 matrix while the modulus showed maximum enhancement of 20% compared to the pristine PA6 resin.

Keywords: Hybrid nanocomposites, PA6, SEBS rubber, toughness.

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Authors: A. Larabi, M. S. Boucherit

Abstract:

In this paper, we show that the association of the PI regulators for the speed and stator currents with a control strategy using the linearization by state feedback for an induction machine without speed sensor, and with an adaptation of the rotor resistance. The rotor speed is estimated by using the model reference adaptive system approach (MRAS). This method consists of using two models: The first is the reference model and the second is an adjustable one in which two components of the stator flux, obtained from the measurement of the currents and stator voltages are estimated. The estimated rotor speed is then obtained by canceling the difference between stator-flux of the reference model and those of the adjustable one. Satisfactory results of simulation are obtained and discussed in this paper to highlight the proposed approach.

Keywords: Asynchronous actuator, PI Regulator, adaptivemethod with reference model, Vector control.

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Authors: S. F. Wong, W. I. Ho, B. Lin, Q. Huang

Abstract:

ERP has been used in many enterprises for management, the accuracy of the production forecasting module is vital to the decision making of the enterprise, and the profit is affected directly. Therefore, enhancing the accuracy of the production forecasting module can also increase the efficiency and profitability. To deal with a lot of data, a suitable, reliable and accurate statistics model is necessary. LSSVM and Grey System are two main models to be studied in this paper, and a case study is used to demonstrate how the combination model is effective to the result of forecasting.

Keywords: ERP, Grey System, LSSVM, production forecasting.

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Authors: Akram Golestani, Mohammad Kazemeini, Farhad Khorasheh, Moslem Fattahi

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Modeling and simulation of fixed bed three-phase catalytic reactors are considered for wet air catalytic oxidation of phenol to perform a comparative numerical analysis between tricklebed and packed-bubble column reactors. The modeling involves material balances both for the catalyst particle as well as for different fluid phases. Catalyst deactivation is also considered in a transient reactor model to investigate the effects of various parameters including reactor temperature on catalyst deactivation. The simulation results indicated that packed-bubble columns were slightly superior in performance than trickle beds. It was also found that reaction temperature was the most effective parameter in catalyst deactivation.

Keywords: Catalyst deactivation, Catalytic wet air oxidation, Trickle-bed, Wastewater.

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Authors: Changjin Xu

Abstract:

In this paper, a delayed prototype model is studied. Regarding the delay as a bifurcation parameter, we prove that a sequence of Hopf bifurcations will occur at the positive equilibrium when the delay increases. Using the normal form method and center manifold theory, some explicit formulae are worked out for determining the stability and the direction of the bifurcated periodic solutions. Finally, Computer simulations are carried out to explain some mathematical conclusions.

Keywords: Prototype model, Stability, Hopf bifurcation, Delay, Periodic solution.

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Authors: A. S. Mousa, F. Shoman

Abstract:

We present a discrete game theoretical model with homogeneous individuals who make simultaneous decisions. In this model the strategy space of all individuals is a discrete and dichotomous set which consists of two strategies. We fully characterize the coherent, split and mixed strategies that form Nash equilibria and we determine the corresponding Nash domains for all individuals. We find all strategic thresholds in which individuals can change their mind if small perturbations in the parameters of the model occurs.

Keywords: Coherent strategy, split strategy, pure strategy, mixed strategy, Nash Equilibrium, game theory.

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Authors: Faramarz Khosravi, Gokhan Izbirak

Abstract:

A weighted statistical stochastic based Analytical Hierarchy Process (AHP) model for modeling the potential barriers and enablers of sustainability for measuring and assessing the sustainability level is proposed. For context-dependent potential barriers and enablers, the proposed model takes the basis of the properties of the variables describing the sustainability functions and was developed into a realistic analytical model for the sustainable behavior of an organization. This thus serves as a means for measuring the sustainability of the organization. The main focus of this paper was the application of the AHP tool in a statistically-based model for measuring sustainability. Hence a strong weighted stochastic AHP based procedure was achieved. A case study scenario of a widely reported major Canadian electric utility was adopted to demonstrate the applicability of the developed model and comparatively examined its results with those of an equal-weighted model method. Variations in the sustainability of a company, as fluctuations, were figured out during the time. In the results obtained, sustainability index for successive years changed form 73.12%, 79.02%, 74.31%, 76.65%, 80.49%, 79.81%, 79.83% to more exact values 73.32%, 77.72%, 76.76%, 79.41%, 81.93%, 79.72%, and 80,45% according to priorities of factors that have found by expert views, respectively. By obtaining relatively necessary informative measurement indicators, the model can practically and effectively evaluate the sustainability extent of any organization and also to determine fluctuations in the organization over time.

Keywords: AHP, sustainability fluctuation, environmental indicators, performance measurement, environmental sustainability.

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Authors: N. A. H. Aizam, V. Uvaraja

Abstract:

The agenda of showing the scheduled time for performing certain tasks is known as timetabling. It is widely used in many departments such as transportation, education, and production. Some difficulties arise to ensure all tasks happen in the time and place allocated. Therefore, many researchers invented various programming models to solve the scheduling problems from several fields. However, the studies in developing the general integer programming model for many timetabling problems are still questionable. Meanwhile, this thesis describes about creating a general model which solves different types of timetabling problems by considering the basic constraints. Initially, the common basic constraints from five different fields are selected and analyzed. A general basic integer programming model was created and then verified by using the medium set of data obtained randomly which is much similar to realistic data. The mathematical software, AIMMS with CPLEX as a solver has been used to solve the model. The model obtained is significant in solving many timetabling problems easily since it is modifiable to all types of scheduling problems which have same basic constraints.

Keywords: AIMMS mathematical software, integer linear programming, scheduling problems, timetabling.

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Authors: S. A. Moeini, M. T.Ahmadian

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Structural behavior of ring stiffened thick walled cylinders made of functionally graded materials (FGMs) is investigated in this paper. Functionally graded materials are inhomogeneous composites which are usually made from a mixture of metal and ceramic. The gradient compositional variation of the constituents from one surface to the other provides an elegant solution to the problem of high transverse shear stresses that are induced when two dissimilar materials with large differences in material properties are bonded. FGM formation of the cylinder is modeled by power-law exponent and the variation of characteristics is supposed to be in radial direction. A finite element formulation is derived for the analysis. According to the property variation of the constituent materials in the radial direction of the wall, it is not convenient to use conventional elements to model and analyze the structure of the stiffened FGM cylinders. In this paper a new cylindrical super-element is used to model the finite element formulation and analyze the static and modal behavior of stiffened FGM thick walled cylinders. By using this super-element the number of elements, which are needed for modeling, will reduce significantly and the process time is less in comparison with conventional finite element formulations. Results for static and modal analysis are evaluated and verified by comparison to finite element formulation with conventional elements. Comparison indicates a good conformity between results.

Keywords: FGMs, Modal analysis, Static analysis, Stiffened cylinders.

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Authors: Nisha Budhwar, Sunita Daniel

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In this paper, we analyse the stability of the SEIR model of malaria with infective immigrants which was recently formulated by the authors. The model consists of an SEIR model for the human population and SI Model for the mosquitoes. Susceptible humans become infected after they are bitten by infectious mosquitoes and move on to the Exposed, Infected and Recovered classes respectively. The susceptible mosquito becomes infected after biting an infected person and remains infected till death. We calculate the reproduction number R0 using the next generation method and then discuss about the stability of the equilibrium points. We use the Lyapunov function to show the global stability of the equilibrium points.

Keywords: Susceptible, exposed, infective, recovered, infective immigrants, reproduction number, Lyapunov function, equilibrium points, global stability.

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Authors: D. I. De Souza, D. R. Fonseca, D. Kipper

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In this paper, the test purpose will be to assess whether or not the accelerated model proposed by Eyring will be able to translate results for the shape and scale parameters of an underlying Weibull model, obtained under two accelerating using conditions, to expected normal using condition results for these parameters. The product being analyzed is a new type of insulate fluid, and the accelerating factor is the voltage stresses applied to the fluid at two different levels (30KV and 40KV). The normal operating voltage is 25KV. In this case, it was possible to test the insulate fluid at normal voltage using condition. Both results for the two parameters of the Weibull model, obtained under normal using condition and translated from accelerated using conditions to normal conditions, will be compared to each other to assess the accuracy of the Eyring model when the accelerating factor is only the voltage stress.

Keywords: Eyring Accelerated Model, Sequential Life Testing, Two-Parameter Weibull Distribution, Voltage Stresses.

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Authors: Amir Alani, Mojtaba Mahmoodian, Anna Romanova, Asaad Faramarzi

Abstract:

Pipelines are extensively used engineering structures which convey fluid from one place to another. Most of the time, pipelines are placed underground and are encumbered by soil weight and traffic loads. Corrosion of pipe material is the most common form of pipeline deterioration and should be considered in both the strength and serviceability analysis of pipes. The study in this research focuses on concrete pipes in sewage systems (concrete sewers). This research firstly investigates how to involve the effect of corrosion as a time dependent process of deterioration in the structural and failure analysis of this type of pipe. Then three probabilistic time dependent reliability analysis methods including the first passage probability theory, the gamma distributed degradation model and the Monte Carlo simulation technique are discussed and developed. Sensitivity analysis indexes which can be used to identify the most important parameters that affect pipe failure are also discussed. The reliability analysis methods developed in this paper contribute as rational tools for decision makers with regard to the strengthening and rehabilitation of existing pipelines. The results can be used to obtain a cost-effective strategy for the management of the sewer system.

Keywords: Reliability analysis, service life prediction, Monte Carlo simulation method, first passage probability theory, gamma distributed degradation model.

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Authors: Guilherme B. B. Vieira, Rafael M. da Silva, Eliana T. P. Senna, Luiz A. S. Senna, Francisco J. Kliemann Neto

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Given the importance of ports as links in the global supply chains and because they are key elements to induce competitiveness in their hinterlands, the number of studies devoted to port governance, management and operations has increased in the last decades. Some of these studies address the port governance model as an element to improve coordination among the actors of the portlogistics chain and to generate a better port performance. In this context, the present study analyzes the governance of Port of Santos through individual interviews with port managers, based on a conceptual model that considers the key dimensions associated with port governance. The results reinforce the usefulness of the applied model and highlight some existing improvement opportunities in the port studied.

Keywords: Port Governance, Model, Port of Santos, Managers’ Perception.

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Authors: Han-Soo Kim, Jae-Gyun Ahn, Hyo-Seung Ahn

Abstract:

Though nonlinear dynamic analysis using a specialized hydro-code such as AUTODYN is accurate and useful tool for progressive collapse assessment of a multi-story building subjected to blast load, it takes too much time to be applied to a practical simulation of progressive collapse of a tall building. In this paper, blast analysis of a RC frame structure using a simplified model with Reinforcement Contact technique provided in Ansys Workbench was introduced and investigated on its accuracy. Even though the simplified model has a fraction of elements of the detailed model, the simplified model with this modeling technique shows similar structural behavior under the blast load to the detailed model. The proposed modeling method can be effectively applied to blast loading progressive collapse analysis of a RC frame structure.

Keywords: Autodyn, Blast Load, Progressive Collapse, Reinforcement Contact.

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Authors: Kang-Hung Yang, Jin-Yuan Hsu

Abstract:

In recent years, several severe large-scale influenza outbreaks happened in many countries, such as SARS in 2005 or H1N1 in 2009. Those influenza Epidemics have greatly impacts not only on people-s life and health, but medical systems in different countries. Although severe diseases are more experienced, they are not fully controlled. Governments have different policies to control the spreads of diseases. However, those policies have both positive and negative social or economical influence on people and society. Therefore, it is necessary and essential to develop an appropriate model for evaluations of policies. Consequently, a proper measure can be implemented to confront the diseases. The main goal of this study is to develop a SIR-based model for the further evaluations of the candidate policies during the influenza outbreaks.

Keywords: SIR, influenza, systems dynamic model, H1N1

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Authors: M. Ntšolo, D. Kalumba, N. Lefu, G. Letlatsa

Abstract:

Rock mass damage due to shear tectonic activity has been investigated largely in geoscience where fluid transport is of major interest. However, little has been studied on the effect of shear zones on rock mass behavior and its impact on stability of rock slopes. At Letšeng Diamonds open pit mine in Lesotho, the shear zone composed of sheared kimberlite material, calcite and altered basalt is forming part of the haul ramp into the main pit cut 3. The alarming rate at which the shear zone is deteriorating has triggered concerns about both local and global stability of pit the walls. This study presents the numerical modelling of the open pit slope affected by shear zone at Letšeng Diamond Mine (LDM). Analysis of the slope involved development of the slope model by using a two-dimensional finite element code RS2. Interfaces between shear zone and host rock were represented by special joint elements incorporated in the finite element code. The analysis of structural geological mapping data provided a good platform to understand the joint network. Major joints including shear zone were incorporated into the model for simulation. This approach proved successful by demonstrating that continuum modelling can be used to evaluate evolution of stresses, strain, plastic yielding and failure mechanisms that are consistent with field observations. Structural control due to geological shear zone structure proved to be important in its location, size and orientation. Furthermore, the model analyzed slope deformation and sliding possibility along shear zone interfaces. This type of approach can predict shear zone deformation and failure mechanism, hence mitigation strategies can be deployed for safety of human lives and property within mine pits.

Keywords: Numerical modeling, open pit mine, shear zone, slope stability.

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Authors: A. Bayaga

Abstract:

This research provides a technical account of estimating Transition Probability using Time-homogeneous Markov Jump Process applying by South African HIV/AIDS data from the Statistics South Africa. It employs Maximum Likelihood Estimator (MLE) model to explore the possible influence of Transition Probability of mortality cases in which case the data was based on actual Statistics South Africa. This was conducted via an integrated demographic and epidemiological model of South African HIV/AIDS epidemic. The model was fitted to age-specific HIV prevalence data and recorded death data using MLE model. Though the previous model results suggest HIV in South Africa has declined and AIDS mortality rates have declined since 2002 – 2013, in contrast, our results differ evidently with the generally accepted HIV models (Spectrum/EPP and ASSA2008) in South Africa. However, there is the need for supplementary research to be conducted to enhance the demographic parameters in the model and as well apply it to each of the nine (9) provinces of South Africa.

Keywords: AIDS mortality rates, Epidemiological model, Time-homogeneous Markov Jump Process, Transition Probability, Statistics South Africa.

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Authors: Jeewanee Bamunusinghe, Damminda Alahakoon

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Visual inputs are one of the key sources from which humans perceive the environment and 'understand' what is happening. Artificial systems perceive the visual inputs as digital images. The images need to be processed and analysed. Within the human brain, processing of visual inputs and subsequent development of perception is one of its major functionalities. In this paper we present part of our research project, which aims at the development of an artificial model for visual perception (or 'understanding') based on the human perceptive and cognitive systems. We propose a new model for perception from visual inputs and a way of understaning or interpreting images using the model. We demonstrate the implementation and use of the model with a real image data set.

Keywords: Image understanding, percept, visual perception.

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Authors: Ahmed Abdolkhalig

Abstract:

This paper examines many mathematical methods for molding the hourly price forward curve (HPFC); the model will be constructed by numerous regression methods, like polynomial regression, radial basic function neural networks & a furrier series. Examination the models goodness of fit will be done by means of statistical & graphical tools. The criteria for choosing the model will depend on minimize the Root Mean Squared Error (RMSE), using the correlation analysis approach for the regression analysis the optimal model will be distinct, which are robust against model misspecification. Learning & supervision technique employed to determine the form of the optimal parameters corresponding to each measure of overall loss. By using all the numerical methods that mentioned previously; the explicit expressions for the optimal model derived and the optimal designs will be implemented.

Keywords: Forward curve, furrier series, regression, radial basic function neural networks.

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